model 1 basic average questions Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (d)

Using Rule 10,

If the average of '$n_1$' numbers is $a_1$ and the average of '$n_2$' numbers is $a_2$, then average of total numbers $n_1$ and $n_2$ is

$Average = {n_1a_1 + n_2a_2}/{n_1 + n_2}$

Students in class A ⇒ x

Students in class B ⇒ y

Students in class C ⇒ z

For classes A and B,

${83x + 76y}/{x+y}$ = 79

⇒ 83x + 76y = 79x + 79y

⇒ 83x – 79x = 79y – 76y

⇒ 4x = 3y

For classes B and C

${76y+85z}/{y+z}$= 81

⇒ 76y + 85z = 81y + 81z

⇒ 5y = 4z

∴ 20x = 15y = 12z

⇒ ${20x}/60$ = ${15y}/60$ = ${12z}/60$

⇒ $x/3$ = $y/4$ = $z/5$

∴ Required average

${83×3+76×4+85×5}/{3+4+5}$

${249+304+425}/12$ = $978/12$

= 81.5

Answer: (d)

Using Rule 2,

If the given observations (x) are occuring with certain frequency (A) then,

$Average = {A_1x_1+A_2x_2+...............+A_nx_n}/{x_1+x_2+......+x_n}$

where, $A_1, A_2, A_3, .......... A_n$ are frequencies

Average height

= ${6×1.15+8×1.1+6×1.12}/20$

= ${6.9+8.8+6.72}/20$ = ${22.42}/20$

= 1 metre 12.1 cm

Answer: (d)

That month will have 5 sundays.

∴ Required average

= ${5×510+25×240}/30$

= ${2550+6000}/30$

= $8550/30$ = 285

Aliter : Using Rule 10,

Here, $n_1$ = 5, $a_1$ = 510

$n_2$ = 25, $a_2$ = 240

Answer: (c)

Using Rule 1,

Average of two or more numbers/quantities is called the mean of these numbers, which is given by

$\text"Average(A)" = \text"Sumof observation / quantities"/\text"No of observation / quantities"$

∴ S = A × n

Mean = ${3 +11+ 9+7+15+ 13+ 8 +19 +17 +21 +14+x}/12$

According to question,

${137+x}/12$ = 12

∴ 137 + x = 144

∴ x = 144 – 137 = 7

Answer: (b)

Let the last number be x.

According to the question,

18 × 10 + 11 × 20 + x = 30 × 15

⇒ 180 + 220 + x = 450

⇒ 400 +x = 450

⇒ x = 450 – 400 = 50

Answer: (a)

Number of successful students in the exam = x

∴ Number of unsuccessful students = 100 – x

According to the question,

30 = ${35x+10(100-x)}/100$

⇒ 3000 = 35x + 1000 – 10x

⇒ 3000 = 25x + 1000

⇒ 25x = 3000 – 1000 = 2000

⇒ x = $2000/25$ = 80